Theme Essential Question: How can you apply and extend the usage of rational numbers when dealing with real world problems?
Essential Questions: How do you justify the algorithms used in integer operations?
Standards: 7. NS.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
7. NS.1a: Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has a 0 charge because its two constituents are oppositely charged.
7. NS.1b: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts
7.NS.1c: Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
7.NS.1d: Apply properties of operations as strategies to add and subtract rational numbers.
This week is to focus on integers (addition and subtraction) and the development strategies/algorithms so that students can develop and apply in the upcoming weeks.
Objectives: The student will model addition and subtraction rules of integers using a number line model and two color counters.
The student will develop the strategies/algorithms for addition integers using prior knowledge, exploring with manipulative and/or discovering from classroom activities.
The student will develop the strategies/algorithms for subtraction integers using prior knowledge, exploring with manipulative and/or discovering from classroom activities.
The student will conclude that subtracting an integer is the same as adding its additive inverse (adding the opposite).
The student will present a viable argument for the development of the algorithm.
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team
At the beginning of the school year the CC committee found it necessary to have students work in cooperative groups from day one. Since the units are project based and involve group work, this first week needs to be used to set up the rules and procedures that you will use for the rest of the school year. Unit 1 will focus on adding, subtracting, multiplying, and dividing RATIONAL numbers. It is advantageous for students to review these operations with integers first, before venturing into doing so with fractions and decimals.
Our purpose is to provide all 7th grade teachers with a curriculum that is useful and workable as we move forward. This section will be used to share comments and suggestions we feel are important. We encourage you to use any highly recommended activities as they meet the recommendations found in the Common Core Curriculum we researched.
We appreciate all the hard work and support we have received from teachers across the district. The suggested lessons, ideas, and products have been very helpful. As we work through these Units in the coming school year please let us know what worked and what didn’t. Please keep us informed about any new products, activities, and/or websites used in lesson development so that they can be added as resources.
We are moving into a new era of math education, not only in the way that we as educators approach the teaching/learning process, but also in the way our students interact with mathematics. We are being asked to help students learn the standards using the eight Mathematical Practices as appropriate. Even though the lesson naturally applies several mathematical practices, this is a new approach both for us and our students. Let’s take it one step at a time. Let’s move together, so we as 7th grade teachers can talk and reflect on our student’s learning. In this first lesson, students are being asked to explore and develop algorithms for the operations of integers that will be later extended to rational numbers. It is an excellent time to talk about Mathematical Practice #7 which states that students should look for and make use of structure.
Background Information Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011)
Using both contextual and numerical problems, students should explore what happens when negatives and positives are combined. Number lines present a visual image for students to explore and record addition and subtraction results. Two-color counters or colored chips can be used as a physical and kinesthetic model for adding and subtracting integers. With one color designated to represent positives and a second color for negatives, addition/subtraction can be represented by placing the appropriate numbers of chips for the addends and their signs on a board. Using the notion of opposites, the board is simplified by removing pairs of opposite colored chips. The answer is the total of the remaining chips with the sign representing the appropriate color. Repeated opportunities over time will allow students to compare the results of adding and subtracting pairs of numbers, leading to the generalization of the rules. Real-world situations could include: profit/loss, money, weight, sea level, debit/credit, football yardage, etc.
Assessment: Product This will be an ongoing product that will be developed during each week of the unit. It is not necessary to begin doing the foldable this week, just prepare the students for the upcoming project.
Foldable
Make a foldable with five divided sections (3 pieces of paper needed). Students will create a section for each of the following:
Addition- Have written rule and examples using integers, fractions, and decimals.
Subtraction- Have written rule and examples using integers, fractions, and decimals.
Multiplication- Have written rule and examples using integers, fractions, and decimals.
Division- Have written rule and examples using integers, fractions, and decimals.
Long Division- Have written rule and examples.
Sample student work adapted from foldable instructions above:
Create a tri-fold for each operation (see samples below)
Students should work in groups of twos or threes to allow for discussion, peer teaching/learning and an opportunity to summarize their ideas in the development of their strategies/algorithms.
Addition tri-fold, student are to give examples to the combinations that will give all possible solutions (i.e. A positive number added to a negative number can results in either a positive or negative number)
Problem examples that correspond to the various combinations (see sample)
Students’ strategies/algorithms
Sketch of physical models
Subtraction tri-fold
Problem examples
Change problems to addition – stress adding the additive inverse (add the opposite). If necessary, have students add this discussion to their tri-fold.
Students’ strategies/algorithms
Sketch of physical models
Key Questions
How does the models, number line and double sided counter, relate to the strategy/algorithm developed for addition of integers?
How does the models, number line and double sided counter, relate to the strategy/algorithm developed for subtraction of integers?
What is mean by adding the additive inverse (ass the opposite) in subtraction problems?
Observable Student Behaviors
The student can demonstrate how adding and subtracting integers can be represented on a number line.
The student can demonstrate how adding and subtracting integers can be represented using two-color counters.
The student can explain their strategy/algorithm for adding and subtracting integers using a model.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary:
Math
Rational Number Additive Inverse Decimals Fractions Integers Negative Numbers Number Line Opposites Positive Numbers
Suggested Activities:
Interactive Classroom Activity with number line, such as the Boat/Shark Game (See your Instructional Facilitator for assistance)
Recommended to support the Boat/Shark game is the Gizmo for add and subtract integers on a number line using dynamic arrows
Hands-On Activity with the use of two-sided counters and the concept of the zero pair (See your Instructional Facilitator for assistance)
Recommended to support the hands-on activity with the two-sided counter is the Gizmo adding and subtracting integers with chips.
Mastering the COMMON CORE in Mathematics Grade 7 by American Book Company
Integers 1.1- p. 1
Absolute Value 1.2- p. 1-2
Opposite Numbers 1.3- p. 2
Adding Integers 1.5-1.7, p 4-6
Subtracting Integers 1.8, p. 7
Multiply and Dividing Integers 1.9-1.11, p. 8 (If time permits during the first week)
Chapter Review p. 9-11
Gizmo Element Builder
Use protons, neutrons, and electrons to build elements. As the number of protons, neutrons, and electrons changes, information such as the name and symbol of the element, the Z, N, and A numbers, the electron dot diagram, and the group and period from the periodic table are shown. Each element is classified as a metal, metalloid, or nonmetal, and its state at room temperature is also given.
Gizmo Real Number Line - Activity A
Use a number line to compare numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers.
Gizmo Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows.
Gizmo Adding and Subtracting Integers with Chips
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction.
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L566 Students typically learn about the concepts of identity, inverse, commutativity, and associativity by exploring the four basic operations (+, –, ×, and ÷) with integers. In this lesson, students investigate these concepts using a geometric model. Moves are performed with a rectangle, and the results of an operation that combines two moves are analyzed. Students determine if the operation is commutative or associative; if an identity element exists; or if there are inverses for any of the moves.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L734 In this lesson, students will adapt expressions that add or subtract two signed integers. This lesson builds on the previous lesson in the unit, where students add/subtract just a positive integer from a signed integer.
Fun with Baseball Stats
http://illuminations.nctm.org/LessonDetail.aspx?ID=L257 The following grades 6-8 activities allow students to explore statistics surrounding baseball. They are exposed to connections between various mathematical concepts and see where this mathematics is used in areas with which they are familiar. This lesson plan is adapted from the May 1996 edition of Mathematics Teaching in the Middle School.
Power Up
http://illuminations.nctm.org/LessonDetail.aspx?ID=L699 Using old batteries and a voltage sensor, students get a real feel of the meaning of negative and positive numbers. Students explore addition of signed numbers by placing batteries end to end (in the same direction or opposite directions) and observe the sum of the batteries’ voltages.
Content: Hands-On Experience with Integer Operations
Theme Essential Question:
How can you apply and extend the usage of rational numbers when dealing with real world problems?
Essential Questions:
How do you justify the algorithms used in integer operations?
Standards:
7. NS.1: Apply and extend previous understandings of addition and subtraction
to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
This week is to focus on integers (addition and subtraction) and the development strategies/algorithms so that students can develop and apply in the upcoming weeks.
Objectives:
The student will model addition and subtraction rules of integers using a number line model and two color counters.
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team
At the beginning of the school year the CC committee found it necessary to have students work in cooperative groups from day one. Since the units are project based and involve group work, this first week needs to be used to set up the rules and procedures that you will use for the rest of the school year. Unit 1 will focus on adding, subtracting, multiplying, and dividing RATIONAL numbers. It is advantageous for students to review these operations with integers first, before venturing into doing so with fractions and decimals.
Our purpose is to provide all 7th grade teachers with a curriculum that is useful and workable as we move forward. This section will be used to share comments and suggestions we feel are important. We encourage you to use any highly recommended activities as they meet the recommendations found in the Common Core Curriculum we researched.
We appreciate all the hard work and support we have received from teachers across the district. The suggested lessons, ideas, and products have been very helpful. As we work through these Units in the coming school year please let us know what worked and what didn’t. Please keep us informed about any new products, activities, and/or websites used in lesson development so that they can be added as resources.
We are moving into a new era of math education, not only in the way that we as educators approach the teaching/learning process, but also in the way our students interact with mathematics. We are being asked to help students learn the standards using the eight Mathematical Practices as appropriate.
Even though the lesson naturally applies several mathematical practices, this is a new approach both for us and our students. Let’s take it one step at a time. Let’s move together, so we as 7th grade teachers can talk and reflect on our student’s learning.
In this first lesson, students are being asked to explore and develop algorithms for the operations of integers that will be later extended to rational numbers. It is an excellent time to talk about Mathematical Practice #7 which states that students should look for and make use of structure.
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011)
Using both contextual and numerical problems, students should explore what happens when negatives and positives are combined. Number lines present a visual image for students to explore and record addition and subtraction results. Two-color counters or colored chips can be used as a physical and kinesthetic model for adding and subtracting integers. With one color designated to represent positives and a second color for negatives, addition/subtraction can be represented by placing the appropriate numbers of chips for the addends and their signs on a board. Using the notion of opposites, the board is simplified by removing pairs of opposite colored chips. The answer is the total of the remaining chips with the sign representing the appropriate color. Repeated opportunities over time will allow students to compare the results of adding and subtracting pairs of numbers, leading to the generalization of the rules. Real-world situations could include: profit/loss, money, weight, sea level, debit/credit, football yardage, etc.
Assessment:
Product
This will be an ongoing product that will be developed during each week of the unit. It is not necessary to begin doing the foldable this week, just prepare the students for the upcoming project.
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Fractions Integers Negative Numbers
Number Line Opposites Positive Numbers
Suggested Activities:
- Interactive Classroom Activity with number line, such as the Boat/Shark Game (See your Instructional Facilitator for assistance)
- Recommended to support the Boat/Shark game is the Gizmo for add and subtract integers on a number line using dynamic arrows
- Hands-On Activity with the use of two-sided counters and the concept of the zero pair (See your Instructional Facilitator for assistance)
- Recommended to support the hands-on activity with the two-sided counter is the Gizmo adding and subtracting integers with chips.
Mastering the COMMON CORE in Mathematics Grade 7 by American Book Company- Integers 1.1- p. 1
- Absolute Value 1.2- p. 1-2
- Opposite Numbers 1.3- p. 2
- Adding Integers 1.5-1.7, p 4-6
- Subtracting Integers 1.8, p. 7
- Multiply and Dividing Integers 1.9-1.11, p. 8 (If time permits during the first week)
- Chapter Review p. 9-11
- Gizmo Element Builder
Use protons, neutrons, and electrons to build elements. As the number of protons, neutrons, and electrons changes, information such as the name and symbol of the element, the Z, N, and A numbers, the electron dot diagram, and the group and period from the periodic table are shown. Each element is classified as a metal, metalloid, or nonmetal, and its state at room temperature is also given.- Gizmo Real Number Line - Activity A
Use a number line to compare numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers.- Gizmo Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows.- Gizmo Adding and Subtracting Integers with Chips
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction.Highly Recommended
- http://illustrativemathematics.org/illustrations/314 (NS.1)
- http://illustrativemathematics.org/illustrations/310 (NS.1)
- http://illustrativemathematics.org/illustrations/46 (NS.1)
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.Diverse Learners:
Homework:
Terminology for Teachers:
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources:
Professional Texts
Literary Texts
Informational Texts
Art, Music, and Media
Manipulatives
Games
Videos
SMART Board Lessons, Promethean Lessons
- Smart Board rational number lessons
http://exchange.smarttech.com/details.html?id=1764f052-3804-448f-9f12-95bc5646a2eaOther Activities, etc.
- Commutative Rectangle
http://illuminations.nctm.org/LessonDetail.aspx?ID=L566Students typically learn about the concepts of identity, inverse, commutativity, and associativity by exploring the four basic operations (+, –, ×, and ÷) with integers. In this lesson, students investigate these concepts using a geometric model. Moves are performed with a rectangle, and the results of an operation that combines two moves are analyzed. Students determine if the operation is commutative or associative; if an identity element exists; or if there are inverses for any of the moves.
- Elevator Arithmetic
http://illuminations.nctm.org/LessonDetail.aspx?ID=L733Students will use vertical movement of an elevator to evaluate signed number expressions.
- Flipping for Integers
http://illuminations.nctm.org/LessonDetail.aspx?ID=L734In this lesson, students will adapt expressions that add or subtract two signed integers. This lesson builds on the previous lesson in the unit, where students add/subtract just a positive integer from a signed integer.
- Fun with Baseball Stats
http://illuminations.nctm.org/LessonDetail.aspx?ID=L257The following grades 6-8 activities allow students to explore statistics surrounding baseball. They are exposed to connections between various mathematical concepts and see where this mathematics is used in areas with which they are familiar. This lesson plan is adapted from the May 1996 edition of Mathematics Teaching in the Middle School.
- Power Up
http://illuminations.nctm.org/LessonDetail.aspx?ID=L699Using old batteries and a voltage sensor, students get a real feel of the meaning of negative and positive numbers. Students explore addition of signed numbers by placing batteries end to end (in the same direction or opposite directions) and observe the sum of the batteries’ voltages.
- Battery Lab
http://illuminations.nctm.org/Lessons/PowerUp/PowerUp-AS-Voltmeter.pdfThis reproducible activity, from an Illuminations lesson, features directions and questions that guide students to place batteries end to end and calculate the sum of the batteries' voltages.
Language
Arts
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
7 Matrix
Accelerated 7
Matrix
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6